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FAWS comments on Open Thread, August 2010-- part 2 - Less Wrong
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The blobs don't reproduce with probability p in any given generation, they reproduce with probability p ever. The scenario doesn't require generations in the sense you seem to be thinking of, it could all happen within 1 second, or a first generation blob might reproduce after the highest generation blob that reproduces has already done so.
Oh, ok. I thought the blobs died each generation. A shrinking population. Instead they go into nursing homes. A growing population which stabilizes once everyone is geriatric.
Got it. Wei pretty clearly has the solution. Negative Binomial distribution
Pretty damned obvious, actually, that (P-N) is distributed as a negative binomial where r is set to N; failure = failure to reproduce; success = birth.